# Potential Flow

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## Potential flow

A fluid flow that is isentropic and that, if incompressible, can be mathematically described by Laplace's equation. For an ideal fluid, or a flow in which viscous effects are ignored, vorticity (defined as the curl of the velocity) cannot be produced, and any initial vorticity existing in the flow simply moves unchanged with the fluid. Ideal fluids, of course, do not exist since any actual fluid has some viscosity, and the effects of this viscosity will be important near a solid wall, in the region known as the boundary layer. Nevertheless, the study of potential flow is important in hydrodynamics, where the fluid is considered incompressible, and even in aerodynamics, where the fluid is considered compressible, as long as shock waves are not present. See Boundary-layer flow, Compressible flow, Isentropic flow

In the absence of viscous effects, a flow starting from rest will be irrotational for all subsequent time. For an irrotational flow, the curl of the velocity is zero (∇ × V = 0). The curl of the gradient of any scalar function is zero (∇ × ∇&phgr; = 0). It then follows mathematically that the condition of irrotationality can be satisfied identically by choosing the scalar function, &phgr;, such that the velocity is the gradient of &phgr; (V = ∇&phgr;). For this reason, this scalar function &phgr; has been traditionally referred to as the velocity potential, and the flow as a potential flow. See Potentials

By applying the continuity equation to the definition of the potential function, it becomes possible to represent the flow by the well-known Laplace equation (∇2&phgr; = 0), instead of the coupled system of the continuity and nonlinear Euler equations. The linearity of the Laplace equation, which also governs other important physical phenomena such as electricity and magnetism, makes it possible to use the principle of superposition to combine elementary solutions in solving more complex problems. See Fluid flow

## Potential Flow

the irrotational flow of a fluid in which each small volume is deformed and displaced progressively without any rotation being present (or vortices developing). A potential flow occurs under certain conditions only for an ideal, frictionless fluid. These conditions occur, for example, when the motion begins from a state of rest and a body immersed in an incompressible fluid begins to move, or when a body strikes the surface of the fluid. In nonideal liquids and gases, a potential flow occurs in those regions where the forces of viscosity are negligible in comparison with those of pressure and no vortices are present. The study of potential flow is greatly simplified in that it involves the determination of only one function of the coordinates and time, called the potential function.

## potential flow

[pə′ten·chəl ′flō]
(fluid mechanics)
Flow in which the velocity of flow is the gradient of a scalar function, known as the velocity potential.
References in periodicals archive ?
The receipt of such a visa increases the potential flow of tourists to Kamchatka.
So, we played with the overall layout to optimise the potential flow in and between the different areas," he says.
Staining of DDGS particles indicated a higher amount of surface layer protein compared with carbohydrate thickness in DDGS particles that had a lower flow function index (which indicated potential flow issues).
Estimates of potential flow rates and internal economic modelling indicate the oil price required for amenable development ranges are \$27 per barrel at the lowest end to \$68, depending on certain assumptions about the deliverability of the reservoir and the cost of structures (and availability) on the North Slope.
Furthermore, adaptive strategy rules, which were developed to predict enemy strategies, used potential flow algorithm to reduce the computational time required for pathfinding (Nguyen, Wang, and Thawonmas 2013).
The results are then compared to potential flow models by Wickern as well as Mercker and Cooper.
While the UK has so far been largely shielded from the crisis in southern Europe, this potential flow can only add to the impact of migration which is already seriously affecting communities across the country.
After Hess and Smith [10], who calculated potential flow around arbitrary bodies, the application of this method rapidly increased.
In the framework of potential flow theory, scientists first restricted their studies to the standing wave solution, which is bounded everywhere.
Users detect potential flow balance issues at an early design stage.
Admitting that the torrent was mainly to blame for the damage, Hasikos said that the riverbed should have been cleaned early, structural walls should have been built and the potential flow should have been calculated.
The pump design offers a potential flow rate of up to 4.

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